A303832 The number of edge-rooted unlabeled connected graphs with n edges.

1, 1, 4, 10, 32, 101, 346, 1220, 4517, 17338, 69107, 285009, 1215015, 5344224, 24223641, 113001129, 541913075, 2668817544, 13484234188, 69831773559, 370361639587, 2009988998148, 11153858854425, 63242354288220, 366140089188603, 2163036956456422, 13031489297543608

Offset

1,3

Links

Table of n, a(n) for n=1..27.

Formula

G.f. A(x) satisfies: A(x)*A000664(x) = A126133(x).

Example

a(1)=1: the connected graph with 1 edge (which is rooted).
a(2)=1: the connected graph with 2 edges (one rooted).
a(3)=4: the triangle graph with one choice of rooting, the linear tree with either the middle or a terminating edge rooted, the star graph with one edge rooted.

Prog

(PARI) \\ See A339063 for G.
seq(n)={my(A=O(x*x^n)); Vec((G(2*n, x+A, [1, 1]) + G(2*n, x+A, [2]))/(2*G(2*n, x+A, [])*(1+x)))} \\ Andrew Howroyd, Nov 21 2020

Crossrefs

Cf. A126133 (not necessarily connected), A000664, A303830 (by number of nodes).

Cf. A002905, A339039, A339040, A339041, A339044.

Sequence in context: A017936 A033297 A129880 * A316103 A137954 A028283

Adjacent sequences: A303829 A303830 A303831 * A303833 A303834 A303835

Keyword

nonn

Author

R. J. Mathar, May 04 2018

Status

approved